Theorem 6 ([1]}) 
Let \(p\colon E\rightarrow M\)  be a map in \({K}/B\) . Suppose that \(p^{-1}V_i\rightarrow V_i\)  is an \(f\) -fibration for each open set \(V_i\)  in a numerable covering \(\lbrace V_i\rbrace _{i\in I}\)  of \(M\) .
Then \(p\)  is an \(f\) -fibration. In particular any fiberwise principal \(G\)  bundle \(\pi \colon P\rightarrow M\)  in \({K}/B\)  over a paracompact base space \(M\) , or more generally
any numerable fiberwise principal \(G\)  bundle in \({K}/B\) , is an \(f\) -fibration.

